MS 101 Alg & Trig test 07 fx • 17 July 2013 Name:

1. 
   1. _____ Jayrick is a descendent of Sepe Nuarpat, born circa 1846. How many biological ancestors does Jayrick have in Sepe Nuarpat's generation?
   2. _____ Jayrick is a descendent of Lalkio Waguk via the family line above Kenye Lebas Tilfas. Via Kenye Lebas Tilfas, how many biological ancestors does Jayrick have in Lalkio's generation?
   3. _____ Jayrick is a descendent of Lalkio Waguk via the family line above Tulensru Tulan Waguk. Via Tulensru Tulan, how many biological ancestors does Jayrick have in Lalkio's generation?
   4. ______________ Which of the above is the actual number of ancestors for Jayrick in Lalkio's generation: the answer to (b), (c), or neither?
   5. f(x) = __________ Write the function that calculates the number of biological ancestors in terms of generation number x.
   6. __________ Pre-contact Kosrae was estimated to have had a population of roughly 6000 people. For what generation number would the number of ancestors for Jayrick be equal to 6000? In other words, solve the function for f(x)=6000.
   7. ______________ Use 25 years for one generation. Based on 25 years per generation, how many years ago did Jayrick's ancestor's number 6000?
2. [t03] A keyboard has 95 characters available for use in passwords:
   
   ABCDEFGHIJKLMNOPQRSTUVWXYZ abcdefghijklmnopqrstuvwxyz 0123456789-= ~!@#$%^&*()_+ ;',./:"<>?[]\{}|.
   
   The strength of a random password as measured by the information entropy. The formula for a random password's information entropy, H, is given by the function:
   
   H = (Length of the password ) log₂(Number of characters available)
   H = L log₂N
   
   where H is reported in bits of entropy. Note that the log is the base 2 logarithm.
   1. H = _____________ bits. For a random password with a length of ten (L = 10) which uses lowercase, uppercase, numbers, and symbols (number of possible characters N to choose from is 95), calculate the bits of entropy.
      
   2. L = _____________ There are some who theorize that the NSA can crack 72 bit passwords and recommend that random passwords have 128 bits of entropy. Use the function above with an N equal to 95 characters. Calculate the length L necessary to obtain H = 128 bits of entropy.
   3. L = _____________ Most computer users only use lowercase and uppercase letters, which is only 52 possible characters for their password. With N equal to 52 characters, Calculate the length L necessary to obtain H = 128 bits of entropy.
   4. _____________ When you learned after test three that your password length was too short to be secure, did you change the password to a longer one? [open answer].
3. The chart depicts a baby weight function for a baby that grew at
   f(x) = 16.07 ln(x) − 27.51 where x is the months since conception and f(x) is the weight in pounds. Birth is at x = 9 months. The y-axis is the weight of the baby in pounds.
   1. ___________ Calculate the weight at x = 24 months.
   2. ____________ Calculate the months for f(x) = 25 pounds.
4. ____________ e⁰
5. ____________ log₇49
6. ____________ log 1000
7. ____________ ln x = 1.60944
8. ____________ e^x = 1096.64
9. ____________ 3 ln (5x) = 12.022
10. ____________ x² − 5² = 12²
11. ____________ log_x4913 = 3
12. 
    

    Distance (m)	Velocity (m/s)
    2	2.7
    5	6
    25	12

    1. The table provides data on the distance versus velocity for a Frisbee flying disk. The data is based loosely on data taken during laboratory 14 by the SC 130 Physical Science students summer 2013. Use a spreadsheet to plot the flying disk data. Add a logarithmic trend line and equation.
       Write the logarithmic function:
       
    2. ________________ Use the logarithmic function to calculate the velocity for a distance of 15 meters.
    3. ________________ Use the logarithmic function to calculate the distance for a velocity of 8 meters per second.
13. _________ Convert π/3 radians to degrees.
14. _________ Convert 135° to radians expressed as π over a number.
15. _________ Calculate the arc length s for a π/3 radian arc with a radius r of 10 meters.
16. _________ The angles inside a triangle add up to 180° If a right triangle has one acute angle of 53°, what is the angle of the other acute angle?
17. _________ Calculate: 100 sin(45°)
18. _________ Calculate: 100 cos(45°)
19. _________ Calculate: 100 tan(45°)
20. _________ Calculate $\arcsin \left(\frac{\sqrt{3}}{2}\right)$, report the result in degrees.
21. θ = __________ For the first throw Iumileen measured a distance of 10 meters horizontally and Jamori read a stopwatch time of 2.0 seconds for a speed of 5 m/s horizontally. The speed of the ball along the ball's flight arc as measured by Deffeny was 8 m/s. Use the diagram to solve for the angle θ.
22. 1. __________ In the movie Pacific Rim the 260 foot tall Jaeger robot Gipsy Danger dragged a ship at an average angle θ as seen in the diagram. Calculate the angle θ. Note: Kaiju were injured in the production of this question.
    2. __________ Gipsy Danger dragged the ship a distance d of 500 meters with a force of 150 megaNewtons. Calculate the energy (work) done in dragging the ship by calculating the dot product using θ calculated above. Disregard the units.
    3. __________ The ship dragged by Gipsy Danger was 60 meters long. Use 60 meters as the length of the lever arm to calculate the torque. Use the same force of 150 megaNewtons, θ calculated above, and the cross product to calculate the torque.
23. 1. ____________ The load vector for Jaeger Striker Eureka's right lead helicopter is given by v = -80i + 95j. Calculate the angle to the vertical θ.
    2. ____________ Calculate the magnitude of the vector v = -80i + 95j.
24. Produce an octagon inscibed in a circle with a center at (0, 0) and a radius of 100 pixels using SVG on your computer oriented as seen in the image. Call me over when you are done and show me your correctly done hexagon in a circle SVG. You must finish this sufficiently prior to the end of the period for me to properly check your result. Write the eight vertex (corner) coordinates below based on an octagon with a center at (0, 0). Start from the coordinate for the top point of the octagon and list the rest of the coordinates clockwise.
    1. ( ________ , _________ )
    2. ( ________ , _________ )
    3. ( ________ , _________ )
    4. ( ________ , _________ )
    5. ( ________ , _________ )
    6. ( ________ , _________ )
    7. ( ________ , _________ )
    8. ( ________ , _________ )
25. If all has gone well, there should be a sheet of paper at the front of the classroom with a RipStik Swizzle wave on the paper along with the number of wavelengths on the paper, the time for that number of wavelengths, the length of the paper, and the vertical distance from the trough to the crest. Use the data to answer the following questions.
    1. λ = _______________ Write the wavelength λ of the RipStik swizzle wave in centimeters.
    2. a = _______________ Calculate the amplitude a of the RipStik swizzle wave.
    3. τ = _______________ Calculate the period τ of the RipStik swizzle wave.
    4. f = _______________ Calculate the frequency f of the RipStik swizzle wave.
    5. b = _______________ Given that $b=\frac{2\pi }{\tau }$, calculate b
    6. y = ______ sin( _________ x). Given the general form y = a sin(bx) and the results above, write the equation for the RipStik swizzle wave.
26. Data from a spring with a weight on the bottom will be recorded on the board. Use that data to answer the following questions.
    1. f = ____________ Calculate the frequency f of the spring.
    2. τ = ____________ Calculate the period τ of the spring.
    3. r = ____________ Calculate the decay rate r of the spring.
    4. f(t) = ____________ e^(−_______________t) sin(______________ t) Write the equation for the spring wave in terms of the time t by filling in the blanks.